Question

A ladder makes an angle of 60° with the floor and its lower end is 2 m from the wall. What is the length of the ladder? At what height is it touching the wall?

Answer 1

Given:

Angle made with floor = 60°

Distance from wall to base of ladder = 2 m

finding:

Length of the ladder

Height at which it touches the wall

Step 1:

= cos(60°) = `"Base"/"hypotenuse"` = `2/"Ladder Length"`

= `1/2 = 2/"Ladder Length"`

= `"Ladder Length" = 2/ (1/2)`

= 4 cm

Step 2:

= sin(60°) = `"Height"/"Ladder Length"` = `"Height"/4`

= `sqrt3/2 = "Height"/4`

= `"Height" = 4 ⋅ sqrt3/2`

= `2sqrt3` m